Meaning of the λ parameter of skew–normal and log–skew normal distributions in fluid geochemistry

The literature related to skew–normal distributions has grown rapidly in recent years but at the moment few applications concern the description of natural phenomena with this type of probability models, as well as the interpretation of their parameters. The skew–normal distributions family represents an extension of the normal family to which a parameter (λ) has been added to regulate the skewness. The development of this theoretical field has followed the general tendency in Statistics towards more flexible methods to represent features of the data, as adequately as possible, and to reduce unrealistic assumptions as the normality that underlies most methods of univariate and multivariate analysis. In this paper an investigation on the shape of the frequency distribution of the logratio ln(Cl−/Na+) whose components are related to waters composition for 26 wells, has been performed. Samples have been collected around the active center of Vulcano island (Aeolian archipelago, southern Italy) from 1977 up to now at time intervals of about six months. Data of the logratio have been tentatively modeled by evaluating the performance of the skew–normal model for each well. Values of the λ parameter have been compared by considering temperature and spatial position of the sampling points. Preliminary results indicate that changes in λ values can be related to the nature of environmental processes affecting the data

Hilbert space on probability density functions with Aitchison geometry

Compositional data analysis motivated the introduction of a complete Euclidean structure in the simplex of D parts. This was based on the early work of J. Aitchison (1986) and completed recently when Aitchinson distance in the simplex was associated with an inner product and orthonormal bases were identified (Aitchison and others, 2002; Egozcue and others, 2003). A partition of the support of a random variable generates a composition by assigning the probability of each interval to a part of the composition. One can imagine that the partition can be refined and the probability density would represent a kind of continuous composition of probabilities in a simplex of infinitely many parts. This intuitive idea would lead to a Hilbert-space of probability densities by generalizing the Aitchison geometry for compositions in the simplex into the set probability densities

Aitchison Geometry for Probability and Likelihood as a new approach to mathematical statistics

The Aitchison vector space structure for the simplex is generalized to a Hilbert space structure A2(P) for distributions and likelihoods on arbitrary spaces. Central notations of statistics, such as Information or Likelihood, can be identified in the algebraical structure of A2(P) and their corresponding notions in compositional data analysis, such as Aitchison distance or centered log ratio transform. In this way very elaborated aspects of mathematical statistics can be understood easily in the light of a simple vector space structure and of compositional data analysis. E.g. combination of statistical information such as Bayesian updating, combination of likelihood and robust M-estimation functions are simple additions/ perturbations in A2(Pprior). Weighting observations corresponds to a weighted addition of the corresponding evidence. Likelihood based statistics for general exponential families turns out to have a particularly easy interpretation in terms of A2(P). Regular exponential families form finite dimensional linear subspaces of A2(P) and they correspond to finite dimensional subspaces formed by their posterior in the dual information space A2(Pprior). The Aitchison norm can identified with mean Fisher information. The closing constant itself is identified with a generalization of the cummulant function and shown to be Kullback Leiblers directed information. Fisher information is the local geometry of the manifold induced by the A2(P) derivative of the Kullback Leibler information and the space A2(P) can therefore be seen as the tangential geometry of statistical inference at the distribution P. The discussion of A2(P) valued random variables, such as estimation functions or likelihoods, give a further interpretation of Fisher information as the expected squared norm of evidence and a scale free understanding of unbiased reasoning

Evaluating the probability and the impact of a failure in GMPLS based networks

In this paper, we define a new scheme to develop and evaluate protection strategies for building reliable GMPLS networks. This is based on what we have called the network protection degree (NPD). The NPD consists of an a priori evaluation, the failure sensibility degree (FSD), which provides the failure probability, and an a posteriori evaluation, the failure impact degree (FID), which determines the impact on the network in case of failure, in terms of packet loss and recovery time. Having mathematical formulated these components, experimental results demonstrate the benefits of the utilization of the NPD, when used to enhance some current QoS routing algorithms in order to offer a certain degree of protection

A new approach to the classification of mammographic masses and normal breast tissue

A new approach to mammographic mass detection is presented in this paper. Although different algorithms have been proposed for such a task, most of them are application dependent. In contrast, our approach makes use of a kindred topic in computer vision adapted to our particular problem. In this sense, we translate the eigenfaces approach for face detection/classification problems to a mass detection. Two different databases were used to show the robustness of the approach. The first one consisted on a set of 160 regions of interest (RoIs) extracted from the MIAS database, being 40 of them with confirmed masses and the rest normal tissue. The second set of RoIs was extracted from the DDSM database, and contained 196 RoIs containing masses and 392 with normal, but suspicious regions. Initial results demonstrate the feasibility of using such approach with performances comparable to other algorithms, with the advantage of being a more general, simple and cost-effective approach

Estimation of the probability of congestion using Monte Carlo method in OPS networks

In networks with small buffers, such as optical packet switching based networks, the convolution approach is presented as one of the most accurate method used for the connection admission control. Admission control and resource management have been addressed in other works oriented to bursty traffic and ATM. This paper focuses on heterogeneous traffic in OPS based networks. Using heterogeneous traffic and bufferless networks the enhanced convolution approach is a good solution. However, both methods (CA and ECA) present a high computational cost for high number of connections. Two new mechanisms (UMCA and ISCA) based on Monte Carlo method are proposed to overcome this drawback. Simulation results show that our proposals achieve lower computational cost compared to enhanced convolution approach with an small stochastic error in the probability estimation

Características fenotípicas de personalidad y neuropsicológicas en padres no afectados de pacientes esquizofrénicos

Introducció. Actualment, està àmpliament acceptat que l'esquizofrènia posseeix una etiologia multifactorial i que existeix una complexa interacció entre factors genètics i factors ambientals. Amb l'objectiu de coneixerà quins són els mecanismes etiològics i patofisiològics que determinen el trastorn una part de la investigaci6 s 'ha centrat, en els últims anys, en la detecció de marcadors de vulnerabilitat en subjectes amb risc al trastorn. Aquesta vulnerabilitat, denominada 'esquizotipia', es pot identificar en subjectes clínicament no afectats. Objectiu. L'objectiu d'aquesta investigació s'ha dirigit a intentar contestar a alguns interrogants que encara no tenen resposta. Per exemple, per què alguns familiars, essent portadors del genotip esquizofrènic, no han presentat mai la malaltia?, existeixen formes esquizotípiques de menor risc per a la presentació del trastorn?, poden alguns patrons esquizotípics 'ajudar' a que la vulnerabilitat es mantingui latent i no es manifesti en forma de trastorn? En termes generals, l'estudi s'ha centrat en la identificació de marcadors de vulnerabilitat dels trastorns de l'espectre esquizofrènic en pares no afectats de pacients amb esquizofrènia (subjectes d'edats avançades amb poca probabilitat de presentar el trastorn) comparats amb pares normals de subjectes normals. Metodologia. S' han avaluat 26 parelles de pares no afectats de pacients amb esquizofrènia i 26 parelles de pares normals de subjectes normals (n= 104) en variables de personalitat i comportamentals (esquizotipia psicomètrica -O-LIFE-, trastorns de personalitat -Qüestionari d'avaluació IPDE-, psicopatologia general -SCL-90- i lloc de control -MHLC-) i variables neuropsicològiques (dèficit atencional -CPT-IP-, funció executiva -TMT part B- i memòria i aprenentatge verbal -CVLT-). Resultats. Els pares dels pacients esquizofrènics, comparats amb els controls, mostren significativament puntuacions mes altes al factor d'anhedònia introvertida, al trastorn paranoide de la personalitat i al trastorn per evitació de la personalitat, més característiques de psicopatologia general i un major lloc de control intern relacionat amb la salut. També realitzen mes errors d'omissió en la tasca atencional, presenten una major interferència proactiva al test de memòria i aprenentatge verbal i mostren una tendència a dedicar mes temps a completar la tasca executiva. Els resultats mostren que les associacions entre les variables de personalitat i les neuropsicològiques són de poca magnitud i les diferències entre ambdós grups no segueixen un patró clarament determinat. Conclusions. Els pares dels pacients esquizofrènics presenten més trets esquizotípics negatius que els pares del subjectes normals. L'anhedònia introvertida podria considerar-se com una forma de menor risc a l'esquizofrènia ja que s'evidencia en subjectes (pares) d'edats avançades que ja han superat l'edat de risc i amb poca probabilitat de presentar mai el trastorn. Tanmateix, es confirma que el trastorn paranoide de la personalitat forma part dels trastorns de l'espectre esquizofrènic. Els pares dels pacients atribueixen un major pes i la internalització i al poder dels altres en relació a l'estat de salut, i en general, presenten més característiques psicopatològiques que el grup control. Quant a les variables neuropsicològiques, els pares dels pacients realitzen pitjor la tasca atencional, són més lents en l'anticipació, planificació i flexibilitat de les respostes en el test executiu. Els indicadors de memòria i aprenentatge verbal no discriminen a ambdós grups, i únicament els pares dels pacients presenten una major interferència proactiva. Finalment, el patró de personalitat i el neuropsicològic corresponen a dos fenotips diferents relacionats amb l'esquizofrènia que no es troben íntimament units en subjectes amb aquestes característiques.

Congestion probability routing in virtual path ATM network

This dissertation focuses on the problem of providing mechanisms for routing point to point and multipoint connections in ATM networks. In general the notion of multipoint connection refers to connections that involve a group of users with more than two members. The main objective of this dissertation is to contribute to design efficient routing protocols with alterative routes in fully connected VP-based ATM Networks for call establishment of point to point and multipoint VC connections. An efficient route should be computed during this connection establishment phase.